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## Question:

Class Participation and Attendance (10%) During the trimester students will discuss various Statistics issues and cases, which are noted in the prescribed textbook. Active student participation in the lectures and tutorials is essential to the learning process. All students are expected to be prepared for and contribute to the lecture and tutorial discussions. To assist in your understanding of Statistics issues, you are encouraged to contribute to in-class discussions. Your participation and interaction with other students will be a major component of the class instruction. Part of your class participation will also be based upon your ability to recognise contemporary statistical issues. As this is a graduate Bachelor of Business unit, regular and active participation in lecture and tutorial discussions is expected from every student each week.

This must include intermediate steps where relevant. Failure to do so will result in a loss of marks. Do not include the assignment questions nor the data with your submitted assignment. Introduction The Assignment Data (LGAData.xls) file contains, LGA data (sourced from ABS) for a population of 400 LGA in Australia. You are required to select a random sample of 50 LGA from this population. Variables in the data set are as below: PN ID number ID V1 LGA name Name V2 Gender Male=1; Female=0 V3 Age Group 30-34 =1; 35-39=2; 39-44 =3; 45-50=4 V4 Age1 number of people 30-34 years old V5 Age2 number of people 35-39 years old V6 Age3 number of people 39-44 years old V7 Age4 number of people 45-50 years old V8 Income category \$650-\$800=0;

\$801-\$850=1 V9 Income1 number of people with \$650-\$800 weekly income V10 Income2 number of people with \$801-\$850 weekly income V11 Occupation type Managers=1; Professionals=2;Sales workers=3;Administration=4 V12 Occupation1 number of Managers V13 Occupation2 number of Professionals V14 Occupation3 number of Sales workers V15 Occupation4 number of Administration V16 Industry of occupation Mining=1; Agriculture=2;Manufacturing=3;Education=4 V17 Industry1 number of people in Mining V18 Industry2 number of people in Agriculture V19 Industry3 number of people in Manufacturing V20 Industry4 number of people in Education V21 Transport 0=car; 1=public transport V22 Living with children 0=with; 1=without Column A (PN), contains the LGA identification numbers from 001 to 400 LGA. 5 Selecting Random Sample and Creating your Sample Data File To select your random sample, you need to open the PopulationLGAData.

Copy and Paste these outputs to your assignment MS- Word document immediately preceding any subsequent analysis. Charts and tables must have appropriate titles and numerical values must be rounded to an appropriate number of decimal places and accompanied by the correct units of measure. Task 1 (10 marks) Use Excel to produce a Frequency Column Chart and; a Relative Frequency Pie-Chart for your sample to show the number and proportion, respectively, of people under each age group. Use these graphical summaries to answer the following questions: (a) How many LGA in your sample indicate use of public transport? (b) Which occupation type occurs most frequently in your sample? (c) What proportion of LGA in your sample consists of people within 30-34 years old age group? Task 2 (10 marks) (a) Use Excel to sort your sample “occupation 4” data.

Use the percentile location formula; LP = (n +1) P 100 , and the three associated rules to determine: (i) The 70th percentile. (ii) The first and third quartiles. Remember to show all working! (b) Briefly explain what the 70th percentile that you have determined informs you about your sample “occupation 4” data. (c) Determine the Inter-Quartile Range of your sample “occupation 4” data and provide a brief explanation of what information this statistic provides about your sample data. 6 Task 3 (15 marks) (a) Use Excel to produce a Descriptive Statistics table for your sample “occupation 4” data. (b) Use results from Task 3 to determine manually for this data, the upper and lower inner fence limits; IFUL = Q3 + 1.5 x IQR IFLL = Q1 – 1.5 x IQR (c) Based on the limits calculated in (b), choose from the numerical summary measures provided in the Descriptive Statistics table, and/or measures calculated previously in

Task 4; (i) an appropriate measure of central tendency, and, (ii) an appropriate measure of dispersion for your sample “occupation 4”data. Remember to show all working! Provide a brief explanation of the reasoning behind your choice in both cases. (d) Write a brief report on the “occupation 4” data paying particular attention, on the mean, median, quartiles and measures of variation. Task 4 (15 marks) Remember to show all working! Failure to do so will result in the loss of marks. (a) From the Descriptive Statistics table obtained in Task 4, identity three pieces of evidence that indicate whether your sample “occupation 4” data has been obtained from a normally distributed population or not. What is your conclusion? Note: Make sure only one piece of evidence relates to the shape of the sample data. (b) Regardless of your conclusion in above, assume the “occupation 4” data is normally distributed.

Applying the Standard Normal tables, calculate how many “occupation 4” observations in your sample would expect to lie within 1.5 standard deviations of the mean (i.e. between z = –1.5 and z = +1.5). (c) Use the mean and standard deviation from the Descriptive Statistics table of Task 4 to calculate the bound for 1.5 standard deviation spread from the mean. Using the “occupation 4” sample data, manually count the number of observations fall within the bound. State whether this count matches, approximately, your answer to (b) and hence whether this result confirms (or not) your conclusion in (a). Task 5 (15 marks) (a) Use Excel to produce a Descriptive Statistics table for the “Occupation 4” variable in your sample suitable for constructing an interval estimate of the population mean “Occupation 4” Hence determine:

(i) A point estimate of the mean “Occupation 4” of the population.
(ii) A 90% confidence interval estimate of the mean “Occupation 4” of the population.
(iii) Make a brief verbal statement explaining the meaning of the confidence interval estimate obtained in
(ii) in the context of the variable in this task.

(b) If the population mean “Occupation 4”is actually 59, would you consider the interval estimate obtained in
(a), to be satisfactory? Explain why or why not. 7 Task 6 (15 marks)
(a) Use Excel to produce a Descriptive Statistics table for the \$650-\$800 income earners in your sample suitable for constructing an interval estimate of the population proportion of income earners. Hence determine:
(i) A point estimate of the proportion of \$650-\$800 income earners in the population.
(ii) A 99% confidence interval estimate of the \$650-\$800 income earners.
(b) Using the following formula: (sample statistic) ? (critical z or t) ? (standard error of the sample statistic) Use the Empirical Rule for a Normal distribution to determine a 95% confidence interval estimate of the \$650-\$800 income earners in the population.
(c) Compare, in terms of the precision, the interval manually calculated in (b) with the interval obtained from the Descriptive Statistics table in
(a). Explain why the direction of the change in precision is expected.

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My Assignment Help. Business Statistics [Internet]. My Assignment Help. 2020 [cited 01 December 2020]. Available from: https://myassignmenthelp.com/free-samples/bb-108-business-statistics/percentile-location-formula.html.

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